The following references represent the state-of-the-art of this invention and are referred to hereinafter.
{1} T. Okamoto, I. Yamaguchi, xe2x80x9cSimultaneous acquisition of spectral image information,xe2x80x9d Opt. Lett., Vol. 16, No. 16, pp. 1277-1279 Aug. 15, 1991.
{2} F. V. Bulygin, G. N. Vishnyakov, G. G. Levin, and D. V. Karpukhin, xe2x80x9cSpectrotomography-a new method of obtaining spectrograms of 2-D objects,xe2x80x9d Optics and Spectroscopy (USSR) Vol. 71(6), pp.561-563, 1991.
{3} T. Okamoto, A. Takahashi, I. Yamaguchi, xe2x80x9cSimultaneous Acquisition of Spectral and Spatial Intensity Distribution,xe2x80x9d Applied Spectroscopy, Vol. 47, No. 8, pp. 1198-1202, Aug. 1993.
{4} M. R. Descour, Non-scanning Imaging Spectrometry, Ph.D Dissertation, University of Arizona, 1994.
{5} M. Descour and E. Dereniak, xe2x80x9cComputed-tomography imaging spectrometer: experimental calibration and reconstruction results,xe2x80x9d Applied Optics, Vol. 34, No. 22, pp. 4817-4826, 1995.
{6} D. W. Wilson, P. D. Maker, and R. E. Muller, xe2x80x9cDesign and Fabrication of Computer-Generated Hologram Dispersers for Computed-Tomography Imaging Spectrometers,xe2x80x9d Optical Society of America Annual Meeting, October 1996.
{7} M. R. Descour, C. E. Volin, E. L. Dereniak, T. M. Gleeson, M. F. Hopkins, D. W. Wilson, and P. D. Maker, xe2x80x9cDemonstration of a computed-tomography imaging spectrometer using a computer-generated hologram disperser,xe2x80x9d Appl. Optics., Vol. 36 (16), pp. 3694-3698, Jun. 1, 1997.
{8} P. D. Maker, and R. E. Muller, xe2x80x9cPhase holograms in polymethyl methacrylate,xe2x80x9d J. Vac. Sci. Technol. B, Vol. 10(6), 2516-2519, November/December 1992.
{9} P. D. Maker and R. E. Muller, xe2x80x9cContinuous Phase and Amplitude Holographic Elements,xe2x80x9d U.S. Pat. No. 5,393,634, Feb. 28, 1995.
{10} P. D. Maker, D. W. Wilson, and R. E. Muller, xe2x80x9cFabrication and performance of optical interconnect analog phase holograms made be electron beam lithography,xe2x80x9d in Optoelectronic Interconnects and Packaging, R. T. Chen and P. S. Guilfoyle, eds., SPIE Proceedings, Vol. CR62, pp. 415-430, February 1996.
{11} F. S. Pool, D. W. Wilson, P. D. Maker, R. E. Muller, J. J. Gill, D. K. Sengupta, J. K. Liu, S. V. Bandara, and S. D. Gunapala, xe2x80x9cFabrication and Performance of Diffractive Optics for Quantum Well Infrared Photodetectors,xe2x80x9d in Infrared Detectors and Focal Plane Arrays V, E. L. Dereniak and R. E. Sampson, Eds. Proc. SPIE Vol. 3379, pp. 402-409, July 1998.
{12} D. W. Wilson, P. D. Maker, R.E. Muller, xe2x80x9cReconstructions of Computed-Tomography Imaging Spectrometer Image Cubes Using Calculated System Matrices,xe2x80x9d in Imaging Spectrometry III, M. R. Descour, S. S. Shen, Eds, Proc. SPIE, Vol. 3118, pp. 184-193, 1997.
{13} D. W. Wilson, P. D. Maker, R. E. Muller, xe2x80x9cCalculation-Based Calibration Procedure for Computed-Tomography Imaging Spectrometers,xe2x80x9d OSA Annual Meeting, Long Beach, Calif., Oct. 14, 1997.
{14} P. D. Maker, R. E. Muller, D. W. Wilson, and P. Mouroulis, xe2x80x9cNew convex grating types manufactured by electron beam lithography,xe2x80x9d 1998 OSA Diffractive Optics Topical Meeting, Kailua-Kona, Hawaii, Jun. 8-11, 1998.
{15} P. Mouroulis, D. W. Wilson, P. D. Maker, and R. E. Muller, xe2x80x9cConvex grating types for concentric imaging spectrometers,xe2x80x9d Appl. Optics, vol. 37, pp. 7200-7208, Nov. 1, 1998.
{16} F. V. Bulygin and G. G. Levin, xe2x80x9cSpectrotomography of Fluorescent Objects,xe2x80x9d Optics and Spectroscopy (USSR), Vol. 84, No.6, pp. 894-897, Aug. 15, 1997.
{17} L. A. Shepp"" and Y. Vardi, xe2x80x9cMaximum likelihood reconstruction for emission tomography,xe2x80x9d IEEE Trans. Med. Imag., MI-1, No. 2, pp 113-122 (1982).
{18} M. R. Descour, B. K. Ford, D. W. Wilson, P. D. Maker, G. H. Bearman, xe2x80x9cHigh-speed spectral imager for imaging transient fluorescence phenomena,xe2x80x9d in Systems and Technologies for Clinical Diagnostics and Drug Discovery, G. E. Cohn, Ed., Proc. SPIE vol. 3259, pp. 11-17, April, 1998.
{19} B. K. Ford, C. E. Volin, M. R. Descour, J. P. Garcia, D. W. Wilson, P. D. Maker, and G. H. Bearman, xe2x80x9cVideo-rate spectral imaging of fluorescence phenomena,xe2x80x9d in Imaging Spectrometry IV, M. R. Descour and S. S. Shen, Eds., Proc. SPIE vol. 3438, p. 313-320, October 1998.
{20} C. E. Volin, B. K. Ford, M. R. Descour, J. P. Garcia, D. W. Wilson, P. D. Maker, and G. H. Bearman, xe2x80x9cHigh-speed spectral imager for imaging transient fluorescence phenomena,xe2x80x9d Applied. Optics, vol. 37, pp. 8112-8119, Dec. 1, 1998.
{21} K. Lange and R. Carson, xe2x80x9cEM Reconstruction Algorithms for Emission and Transmission Tomography,xe2x80x9d Journal of Computer Assisted Tomography, vol. 8, no. 2, pp. 306-316, April 1984.
{22} U.S. Pat. No. 3,748,015 to Offner, Jul. 24, 1973.
{23} U.S. Pat. No. 5,880,834 to Chrisp, Mar. 9, 1999.
{24} L. Mertz, xe2x80x9cConcentric spectrographs,xe2x80x9d Appl. Optics, Vol. 16, No. 12, pp. 3122-3124, Dec. 1977.
{25} F. V. Bulygin and G. G. Levin, xe2x80x9cSpectral of 3-D objects,xe2x80x9d Optics and Spectroscopy (USSR), Vol. 79, No.6, pp. 890-894, 1995.
{26} M. R. Descour and E. L. Dereniak, xe2x80x9cNonscanning no-moving-parts imaging spectrometer,xe2x80x9d SPIE Vol. 2480, pp. 48-64, Jan. 1995.
{27} M. R. Descour, R. A Schowengerdt, E. L. Dereniak, K. J. Thome, A. B. Schumacher, D. W. Wilson and P. D. Maker xe2x80x9cAnalysis of the Computed-Tomography Imaging Spectrometer by singular value decomposition,xe2x80x9d SPIE Vol. 2758, pp. 127-133, Jan. 1996.
{28} M. R. Descour, C. E. Volin, E. L. Dereniak and K. J. Thome, xe2x80x9cDemonstration of a high-speed nonscanning imaging spectrometer,xe2x80x9d Opt. Lett., Vol. 22, No. 16, pp. 1271-1273 Aug. 15, 1997.
The above numbered references are referred to hereinafter by their number N enclosed in special brackets, e.g. {10} or where multiple references are referred to by their numbers, e.g. {2, 16, 25}.
A type of spectrometer known in the field of optics as a xe2x80x9ccomputed tomography imaging spectrometerxe2x80x9d, or CTIS hereinafter, enables transient-event spectral imaging by capturing spatial and spectral information in a single snapshot. This has been accomplished by imaging a scene through a two-dimensional (2D) grating disperser as illustrated in the prior-art transmissive system 30 of FIG. 1.
Referring to FIGS. 1-3, in this invention a primary optical system forms a real image 40 of the scene on a rectangular aperture 31 that serves as a field stop 41. Since primary optical systems are well known in the art, for example telescopes, microscopes, endoscopes, etc., such systems are not shown in the drawings.
For example, in FIG. 2, spots of visible light, namely a blue spot B, a red spot R and a white spot W, in the field stop 41 are collimated in a lens 32, filtered through a wide-band filter means 33, and passed through a 2D grating disperser 34 which produces a 2D array of diffraction orders 35. A final focusing element, such as lens 36, re-images the various diffraction orders of light 37 onto a focal plane array (FPA) detector 38, e.g. a charge coupled device, that records the intensity but not the color of the incident light. Each diffraction order transmitted from grating disperser 34 produces a spectrally dispersed image 44 of the scene, except for the undiffracted xe2x80x9czerothxe2x80x9d order which produces an undispersed image in the dashed center area 45 of FPA detector 38 as illustrated in FIG. 3.
A prior art technique can be used to reconstruct the spectra of all the points in the object scene from the captured intensity pattern and knowledge of how points and wavelengths in the field stop map to pixels on the detector. This reconstruction problem is mathematically similar to that encountered in three-dimensional volume imaging in medicine. Hence it is possible to reconstruct the pixel spectra from a CTIS image by one of several iterative algorithms that have been developed for medical emission tomography {17, 21}. In this prior art technique, there are no moving parts or narrow-band filters, and a large fraction of collected light is passed to the detector at all times with CTIS.
Therefore, the disadvantage with current imaging spectrometers is that they are used to perform either (1) spatial scanning through a slit, i.e. a one-dimensional aperture thereby producing spectra in a line or a one-dimensional spectra, or (2) spectral scanning through a narrow-band filter which causes both loss of signal and data corruption for transient scenes.
A CTIS instrument can be made compact, rugged, and reliable, and can be used wherever spectral imaging is needed. The CTIS instrument concept originated in Japan {1, 3} and Russia {2, 16, 25}, and has been advanced by Jet Propulsion Laboratory (JPL) and others {4, 5, 7, 12, 18-20, 26-28}.
The heart of the prior art computed-tomography imaging spectrometer is the two-dimensional grating disperser 34. In all implementations preceding that by JPL {12} and Descour et al. {7}, the two-dimensional grating disperser was realized by stacking and crossing one-dimensional transmissive gratings.
This type of spectrometer had a number of disadvantages, namely (1) the total throughput efficiency was low, (2) only a few diffracted orders contained most of the intensity and saturated the FPA detector 38, and (3) the pattern of dispersed images did not fill the FPA detector area efficiently.
JPL overcame all of these problems by using a computer-generated hologram (CGH) disperser {7}. JPL""s CTIS-specific CGH design algorithms generated designs having high total efficiency and nearly arbitrary patterns of order efficiencies. To accurately fabricate such computer-generated holograms, JPL developed an analog direct-write electron-beam lithography technique that requires only a single development step {8, 10}. This technique allowed JPL to produce fine-featured surface-relief profiles in thin films of polymethyl methacrylate (PMMA). Diffractive optical elements fabricated by such E-beam method demonstrated better performance than elements fabricated by optical lithography or laser writing. For infrared applications that required deeper structures than the E-beam technique could produce, JPL demonstrated the capability of transferring the PMMA surface profile with depth amplification into GaAs semiconductor wafers by reactive ion etching {11}.
Prior to reconstructing the spectra of unknown scenes, a CTIS system had to be calibrated. In other words, the process in which points of light in the field stop 41, were propagated through the spectrometer system and were recorded by the detector 38 had to be determined.
Since the light entering the field stop was polychromatic, there was actually a three-dimensional input to the system, i.e. spatial dimensions x and y, and wavelength dimension lambda, xcex. To make the problem manageable, the three dimensional spatial-spectral volume was subdivided into small voxels {5} as shown in FIG. 4 {13}. The term xe2x80x9cvoxelxe2x80x9d as used herein means a spatial spectral sub-volume element. Calibration then became the determination of which detector pixels were illuminated by a given scene voxel and with what strength, which is referred to herein as xe2x80x9cscene-voxel to detector-pixel mappingxe2x80x9d.
This scene-voxel to detector-pixel mapping is represented as a system transfer matrix H that has nd rows and ns columns, where nd is the number of detector pixels and ns is the number of scene voxels. For any given scene S composed of voxels s=1 . . . ns, the detector image D composed of pixels d=1 . . . nd is given by the matrix equation D=Hxc2x7S, where S and D are arranged as column vectors and all sources of noise have been ignored.
In this invention the technique for calibrating CTIS systems is a combination of measurements with numerical simulations. First, the efficiency of the system is measured at all wavelengths, and in all diffraction orders, but at only one spatial location in the field stop. This is done by placing a monochromator-illuminated optical fiber in the center of a field stop, and recording detector images for many wavelengths in the spectral band of interest, e.g. 450-750 nm.
Each of these detector images is then computer analyzed to determine the efficiency, position, and aberrations, if severe, of each diffraction order at the given wavelength. It should be noted that this measurement included the spectrally dependent transmission of all the optical elements and the responsivity of the focal plane array detector.
With the system efficiency known, we then used simulation to derive the system transfer matrix H that maps voxels in the field stop to pixels on the detector. This is accomplished by tracing many rays from each voxel through the system, utilizing the measured information and keeping track of the resulting scene-voxel to detector-pixel connection weights. This simulation step can be replaced with actual measurements of scene-voxel to detector-pixel mappings by moving the fiber to each spatial location within the object scene plane. However, this increases the effort significantly and does not allow the voxel sizes (scene resolution) to be adjusted after calibration.
Once the system transfer matrix H is known, unknown scenes could then be imaged and their spectra reconstructed. We used an iterative expectation-maximization (EM) algorithm {5}. This algorithm had been developed for reconstructing positron-emission tomography medical images {17, 21}, but other known emission tomography algorithms are also applicable.
The reconstruction is started with an initial estimate for the scene S that is typically unity. Then a predicted detector vector Dp is calculated,
Dp=Hxc2x7S xe2x80x83xe2x80x83(1) 
Corrections are then made to the scene based on the back projection of the ratio of the measured detector and predicted detector,
sxe2x80x2j=(sj/sumi(Hi,j))xc2x7(HTxc2x7(Dm/Dp))j xe2x80x83xe2x80x83(2) 
for j=1 . . .ns 
where sumi indicates a summation over i for each transfer matrix component Hi,j, HT is the transpose of H, Dm is the measured detector image, Dp is the predicted detector image, and where the ratio of the D vectors is performed element by element. The parameter sxe2x80x2, in Eq. (2) signifies that it is the next iteration of s. If Dm=Dp, then the correction factor becomes unity and there is no change to S. Eq. (1) and Eq. (2) are then used iteratively until the predicted detector matched the measured detector to a desired error tolerance or until the improvement stagnates. Typically 10-30 iterations were required for acceptable scene reconstructions.
Referring to FIGS. 5-7, to illustrate the feasibility of the reconstructive feature of this invention, a test simulation was conducted with a scene of overlapping monochromatic numbers 1 to 10 as shown in FIG. 5 {6, 13}. FIG. 5, therefore, depicts an arbitrary artificial multi-spectral scene which, with CTIS, became a focal plane array image of a CTIS-dispersed scene as shown in FIG. 6. Tomographic reconstruction of the focal plane array image of FIG. 6 was used to convert the image into spatial and spectral data consisting of wavelengths over 10 bands each comprising 32xc3x9732 pixels as shown in FIG. 7.
To illustrate the use of this invention for spectral imaging of transient scenes, an experiment was conducted as follows. A transmissive CTIS system was constructed and calibrated as described above. FIG. 8 is a diagram of the CTIS system having a charge-coupled device (CCD) camera 100, a re-imaging lens unit 101, assembly 102 comprising a 2D transmissive grating and wide-band filters, collimating lens unit 103, object scene aperture unit 104, and primary imaging lens unit 105. In one embodiment, CCD camera 100 has 768xc3x97480 pixels, with shutter speed of 30 frames/sec., lens unit 101 has a 25 mm focal length, unit 102 passes and disperses 450 nm-750 nm wavelengths, lens unit 103 has a 75 mm focal length, aperture unit 104 is 2.5 mmxc3x972.5 mm square, and lens unit 105 has a 25 mm focal length.
A scene consisting of 4 colored letters, namely a red letter R, a yellow letter Y, a green letter G, and a blue letter B, on a circular disc having a black background 110 as shown in FIG. 9, was mounted on a platform rotating at a speed such that the human eye could not discern individual letters. Camera 100 was set to have an exposure time short enough to freeze the action in the scene and record an image.
The image captured by CTIS detector 115 was transferred to computer 116 and reconstructed into 62xc3x9772 pixelsxc3x9730 spectral bands (10 nm/band) . FIG. 10 shows the actual reconstructed panchromatic image in black and white (summation of all bands for each pixel) with colors reversed to lighten the image, and FIG. 11 shows the average spectra of the each of the colored letters R, Y, G and B (red, yellow, green and blue, respectively) shown in FIG. 9. In our process, and in this example, the CTIS algorithm was improved by using our xe2x80x9cundiffracted image constraintxe2x80x9d process of this invention which is discussed more fully below.
Having demonstrated feasibility of the CTIS technique for visible wavelengths, the following demonstrates how CTIS feasibility can extended to cover the entire ultraviolet to long-wave infrared portion of the spectrum.
Prior art CTIS systems have been transmissive in nature and thus require refractive lenses. The problem with a transmissive design is that for operation in the ultraviolet and infrared portions of the spectrum, there are few materials that transmit well. Hence it is more difficult to design achromatized lenses. Furthermore, multi-element refractive lenses can become large and heavy, severely limiting the range of applications.
Since reflective systems do not exhibit chromatic aberration and are thus relatively easy to scale to different wavelengths, we found, in this invention, that we could overcome these problems with the transmissive system by designing a reflective CTIS based on the Offner design.
The Offner design is a particular reflective configuration that consists of two concentric mirrors (U.S. Pat. No. 3,748,015 {22}). Traditional xe2x80x9cslit imagingxe2x80x9d spectrometers based on the Offner design, see for example U.S. Pat. No. 5,880,834 {23}, have become popular in recent years because they can be made very compact and exhibit excellent imaging. However, the difficulty with the Offner form is that it requires the grating to be fabricated on a convex surface {23}. U.S. Pat. Nos. 3,748,015 and 5,880,834 are hereby incorporated herein by reference to show portions of various optical arrangements which can be used in this invention.
In our Offner design, we had recently improved our E-beam technique to allow fabrication on non-flat substrates {14, 15}, thereby producing ruled or xe2x80x9cone-dimensionalxe2x80x9d gratings. Such convex blazed gratings demonstrated higher efficiency and lower scattered light than diamond-ruled and holographic gratings as used in U.S. Pat. No. 5,880,834 {23}.
In one embodiment of this invention, we improved the prior art CTIS. We achieved superior results when we started the iterative process with an initial estimate used in Eq. (1) that was the product of the measured undiffracted spatial image with unity spectra.
With regard to the CTIS reconstruction algorithm, it was known that medical images reconstructed using the EM algorithm can develop edge effects and noise as the iterations proceed. Researchers in the positron-emission tomography community had developed a number of techniques to suppress such degrading effects. In this invention, however, we found that such artifacts can be minimized in CTIS reconstructions by constraining the solution so that the scene summed along the spectral dimension, with proper spectral weighting, agreed with the measured undiffracted image. The constraint uses the measured spatial information in the scene to reduce the dimensionality of the unknown information. Hence it produces more accurate spectra in addition to reducing spatial artifacts. We refer to our improvement for producing a reconstructed spectral and spatial object scene as reconstructing the object scene with xe2x80x9cundiffracted image constraint.xe2x80x9d
The term xe2x80x9cundiffracted image constraintxe2x80x9d process as used herein means that the following additional steps are performed while reconstructing the image scene:
(a) calculating the predicted undiffracted image based on the current estimate of the scene; thereafter
(b) calculating a new set of scaling factors for the scene that force the predicted undiffracted image to equal the measured undiffracted image; and thereafter
(c) uniformly scaling the entire scene so that the total number of photons in a predicted detector image remains constant from iteration to iteration.
Thereafter, the process for reconstructing the image scene resumes at Eq. 1.
The following is an example of our undiffracted image constraint process. After equation (2) is performed, the new predicted undiffracted image is calculated as follows:
Dpundif=Hundifxc2x7Sxe2x80x2xe2x80x83xe2x80x83(3) 
where Hundif is the part of the system transfer matrix that maps to the undiffracted order. To force agreement between the predicted and measured undiffracted images, we scale all the scene voxels that contribute to a given undiffracted image pixel (x,y). The scaling factor is the ratio of the measured and predicted (x,y)th pixels in the undiffracted image as follows:
sxe2x80x3x,y,xcex=dmundifx,y/dpundifx,yxc2x7sxe2x80x2x,y,xcexx=1 . . . nx, y=1 . . . ny, xcex=1 . . . nxcexxe2x80x83xe2x80x83(4) 
where x and y are the spatial indices and xcex is the spectral band index. Note that the same scaling factor is used for all voxels with the same spatial location. This is because the undiffracted image is just a weighted sum along the spectral dimension of the scene voxel cube (FIG. 4). This weighted sum is calculated in Eq. 3. The application of Eq. (4) creates an energy imbalance compared to the original predicted scene S. To correct this imbalance, we scale the entire scene so that the energy that falls on the detector is conserved from iteration to iteration,
Sxe2x80x3xe2x80x2=Sxe2x80x3xc2x7sum(Hxc2x7S)/sum(Hxc2x7Sxe2x80x3) xe2x80x83xe2x80x83(5) 
We have found that our improved CTIS process for imposing the undiffracted image constraint works well in practice.
In a alternative embodiment of this invention, the process constrains the maximization step (Eq. 2) of the EM algorithm, so as to find S that minimizes the error in Dm=Hxc2x7S subject to the constraint that Dmundif=Hundifxc2x7S. One technique used for finding solutions to this type of problem is the method of Lagrange multipliers.
Other experiments have been performed that compare CTIS reconstructed spectra to known spectra of emission and reflectance targets. In most cases, agreement to within approximately xc2x15% is obtained throughout the CTIS wavelength band of operation.